// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2015 Jianwei Cui <thucjw@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_CXX11_TENSOR_TENSOR_FFT_H
#define EIGEN_CXX11_TENSOR_TENSOR_FFT_H

namespace Eigen {

/** \class TensorFFT
 * \ingroup CXX11_Tensor_Module
 *
 * \brief Tensor FFT class.
 *
 * TODO:
 * Vectorize the Cooley Tukey and the Bluestein algorithm
 * Add support for multithreaded evaluation
 * Improve the performance on GPU
 */

template<bool NeedUprade>
struct MakeComplex
{
	template<typename T>
	EIGEN_DEVICE_FUNC T operator()(const T& val) const
	{
		return val;
	}
};

template<>
struct MakeComplex<true>
{
	template<typename T>
	EIGEN_DEVICE_FUNC std::complex<T> operator()(const T& val) const
	{
		return std::complex<T>(val, 0);
	}
};

template<>
struct MakeComplex<false>
{
	template<typename T>
	EIGEN_DEVICE_FUNC std::complex<T> operator()(const std::complex<T>& val) const
	{
		return val;
	}
};

template<int ResultType>
struct PartOf
{
	template<typename T>
	T operator()(const T& val) const
	{
		return val;
	}
};

template<>
struct PartOf<RealPart>
{
	template<typename T>
	T operator()(const std::complex<T>& val) const
	{
		return val.real();
	}
};

template<>
struct PartOf<ImagPart>
{
	template<typename T>
	T operator()(const std::complex<T>& val) const
	{
		return val.imag();
	}
};

namespace internal {
template<typename FFT, typename XprType, int FFTResultType, int FFTDir>
struct traits<TensorFFTOp<FFT, XprType, FFTResultType, FFTDir>> : public traits<XprType>
{
	typedef traits<XprType> XprTraits;
	typedef typename NumTraits<typename XprTraits::Scalar>::Real RealScalar;
	typedef typename std::complex<RealScalar> ComplexScalar;
	typedef typename XprTraits::Scalar InputScalar;
	typedef
		typename conditional<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar>::type
			OutputScalar;
	typedef typename XprTraits::StorageKind StorageKind;
	typedef typename XprTraits::Index Index;
	typedef typename XprType::Nested Nested;
	typedef typename remove_reference<Nested>::type _Nested;
	static const int NumDimensions = XprTraits::NumDimensions;
	static const int Layout = XprTraits::Layout;
	typedef typename traits<XprType>::PointerType PointerType;
};

template<typename FFT, typename XprType, int FFTResultType, int FFTDirection>
struct eval<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>, Eigen::Dense>
{
	typedef const TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>& type;
};

template<typename FFT, typename XprType, int FFTResultType, int FFTDirection>
struct nested<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>,
			  1,
			  typename eval<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>>::type>
{
	typedef TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection> type;
};

} // end namespace internal

template<typename FFT, typename XprType, int FFTResultType, int FFTDir>
class TensorFFTOp : public TensorBase<TensorFFTOp<FFT, XprType, FFTResultType, FFTDir>, ReadOnlyAccessors>
{
  public:
	typedef typename Eigen::internal::traits<TensorFFTOp>::Scalar Scalar;
	typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
	typedef typename std::complex<RealScalar> ComplexScalar;
	typedef typename internal::conditional<FFTResultType == RealPart || FFTResultType == ImagPart,
										   RealScalar,
										   ComplexScalar>::type OutputScalar;
	typedef OutputScalar CoeffReturnType;
	typedef typename Eigen::internal::nested<TensorFFTOp>::type Nested;
	typedef typename Eigen::internal::traits<TensorFFTOp>::StorageKind StorageKind;
	typedef typename Eigen::internal::traits<TensorFFTOp>::Index Index;

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorFFTOp(const XprType& expr, const FFT& fft)
		: m_xpr(expr)
		, m_fft(fft)
	{
	}

	EIGEN_DEVICE_FUNC
	const FFT& fft() const { return m_fft; }

	EIGEN_DEVICE_FUNC
	const typename internal::remove_all<typename XprType::Nested>::type& expression() const { return m_xpr; }

  protected:
	typename XprType::Nested m_xpr;
	const FFT m_fft;
};

// Eval as rvalue
template<typename FFT, typename ArgType, typename Device, int FFTResultType, int FFTDir>
struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, Device>
{
	typedef TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir> XprType;
	typedef typename XprType::Index Index;
	static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
	typedef DSizes<Index, NumDims> Dimensions;
	typedef typename XprType::Scalar Scalar;
	typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
	typedef typename std::complex<RealScalar> ComplexScalar;
	typedef typename TensorEvaluator<ArgType, Device>::Dimensions InputDimensions;
	typedef internal::traits<XprType> XprTraits;
	typedef typename XprTraits::Scalar InputScalar;
	typedef typename internal::conditional<FFTResultType == RealPart || FFTResultType == ImagPart,
										   RealScalar,
										   ComplexScalar>::type OutputScalar;
	typedef OutputScalar CoeffReturnType;
	typedef typename PacketType<OutputScalar, Device>::type PacketReturnType;
	static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;
	typedef StorageMemory<CoeffReturnType, Device> Storage;
	typedef typename Storage::Type EvaluatorPointerType;

	enum
	{
		IsAligned = false,
		PacketAccess = true,
		BlockAccess = false,
		PreferBlockAccess = false,
		Layout = TensorEvaluator<ArgType, Device>::Layout,
		CoordAccess = false,
		RawAccess = false
	};

	//===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
	typedef internal::TensorBlockNotImplemented TensorBlock;
	//===--------------------------------------------------------------------===//

	EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
		: m_fft(op.fft())
		, m_impl(op.expression(), device)
		, m_data(NULL)
		, m_device(device)
	{
		const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
		for (int i = 0; i < NumDims; ++i) {
			eigen_assert(input_dims[i] > 0);
			m_dimensions[i] = input_dims[i];
		}

		if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
			m_strides[0] = 1;
			for (int i = 1; i < NumDims; ++i) {
				m_strides[i] = m_strides[i - 1] * m_dimensions[i - 1];
			}
		} else {
			m_strides[NumDims - 1] = 1;
			for (int i = NumDims - 2; i >= 0; --i) {
				m_strides[i] = m_strides[i + 1] * m_dimensions[i + 1];
			}
		}
		m_size = m_dimensions.TotalSize();
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }

	EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data)
	{
		m_impl.evalSubExprsIfNeeded(NULL);
		if (data) {
			evalToBuf(data);
			return false;
		} else {
			m_data = (EvaluatorPointerType)m_device.get(
				(CoeffReturnType*)(m_device.allocate_temp(sizeof(CoeffReturnType) * m_size)));
			evalToBuf(m_data);
			return true;
		}
	}

	EIGEN_STRONG_INLINE void cleanup()
	{
		if (m_data) {
			m_device.deallocate(m_data);
			m_data = NULL;
		}
		m_impl.cleanup();
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffReturnType coeff(Index index) const { return m_data[index]; }

	template<int LoadMode>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketReturnType packet(Index index) const
	{
		return internal::ploadt<PacketReturnType, LoadMode>(m_data + index);
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const
	{
		return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);
	}

	EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return m_data; }
#ifdef EIGEN_USE_SYCL
	// binding placeholder accessors to a command group handler for SYCL
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler& cgh) const { m_data.bind(cgh); }
#endif

  private:
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalToBuf(EvaluatorPointerType data)
	{
		const bool write_to_out = internal::is_same<OutputScalar, ComplexScalar>::value;
		ComplexScalar* buf =
			write_to_out ? (ComplexScalar*)data : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * m_size);

		for (Index i = 0; i < m_size; ++i) {
			buf[i] = MakeComplex<internal::is_same<InputScalar, RealScalar>::value>()(m_impl.coeff(i));
		}

		for (size_t i = 0; i < m_fft.size(); ++i) {
			Index dim = m_fft[i];
			eigen_assert(dim >= 0 && dim < NumDims);
			Index line_len = m_dimensions[dim];
			eigen_assert(line_len >= 1);
			ComplexScalar* line_buf = (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * line_len);
			const bool is_power_of_two = isPowerOfTwo(line_len);
			const Index good_composite = is_power_of_two ? 0 : findGoodComposite(line_len);
			const Index log_len = is_power_of_two ? getLog2(line_len) : getLog2(good_composite);

			ComplexScalar* a =
				is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * good_composite);
			ComplexScalar* b =
				is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * good_composite);
			ComplexScalar* pos_j_base_powered =
				is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * (line_len + 1));
			if (!is_power_of_two) {
				// Compute twiddle factors
				//   t_n = exp(sqrt(-1) * pi * n^2 / line_len)
				// for n = 0, 1,..., line_len-1.
				// For n > 2 we use the recurrence t_n = t_{n-1}^2 / t_{n-2} * t_1^2

				// The recurrence is correct in exact arithmetic, but causes
				// numerical issues for large transforms, especially in
				// single-precision floating point.
				//
				// pos_j_base_powered[0] = ComplexScalar(1, 0);
				// if (line_len > 1) {
				//   const ComplexScalar pos_j_base = ComplexScalar(
				//       numext::cos(M_PI / line_len), numext::sin(M_PI / line_len));
				//   pos_j_base_powered[1] = pos_j_base;
				//   if (line_len > 2) {
				//     const ComplexScalar pos_j_base_sq = pos_j_base * pos_j_base;
				//     for (int i = 2; i < line_len + 1; ++i) {
				//       pos_j_base_powered[i] = pos_j_base_powered[i - 1] *
				//           pos_j_base_powered[i - 1] /
				//           pos_j_base_powered[i - 2] *
				//           pos_j_base_sq;
				//     }
				//   }
				// }
				// TODO(rmlarsen): Find a way to use Eigen's vectorized sin
				// and cosine functions here.
				for (int j = 0; j < line_len + 1; ++j) {
					double arg = ((EIGEN_PI * j) * j) / line_len;
					std::complex<double> tmp(numext::cos(arg), numext::sin(arg));
					pos_j_base_powered[j] = static_cast<ComplexScalar>(tmp);
				}
			}

			for (Index partial_index = 0; partial_index < m_size / line_len; ++partial_index) {
				const Index base_offset = getBaseOffsetFromIndex(partial_index, dim);

				// get data into line_buf
				const Index stride = m_strides[dim];
				if (stride == 1) {
					m_device.memcpy(line_buf, &buf[base_offset], line_len * sizeof(ComplexScalar));
				} else {
					Index offset = base_offset;
					for (int j = 0; j < line_len; ++j, offset += stride) {
						line_buf[j] = buf[offset];
					}
				}

				// process the line
				if (is_power_of_two) {
					processDataLineCooleyTukey(line_buf, line_len, log_len);
				} else {
					processDataLineBluestein(line_buf, line_len, good_composite, log_len, a, b, pos_j_base_powered);
				}

				// write back
				if (FFTDir == FFT_FORWARD && stride == 1) {
					m_device.memcpy(&buf[base_offset], line_buf, line_len * sizeof(ComplexScalar));
				} else {
					Index offset = base_offset;
					const ComplexScalar div_factor = ComplexScalar(1.0 / line_len, 0);
					for (int j = 0; j < line_len; ++j, offset += stride) {
						buf[offset] = (FFTDir == FFT_FORWARD) ? line_buf[j] : line_buf[j] * div_factor;
					}
				}
			}
			m_device.deallocate(line_buf);
			if (!is_power_of_two) {
				m_device.deallocate(a);
				m_device.deallocate(b);
				m_device.deallocate(pos_j_base_powered);
			}
		}

		if (!write_to_out) {
			for (Index i = 0; i < m_size; ++i) {
				data[i] = PartOf<FFTResultType>()(buf[i]);
			}
			m_device.deallocate(buf);
		}
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static bool isPowerOfTwo(Index x)
	{
		eigen_assert(x > 0);
		return !(x & (x - 1));
	}

	// The composite number for padding, used in Bluestein's FFT algorithm
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Index findGoodComposite(Index n)
	{
		Index i = 2;
		while (i < 2 * n - 1)
			i *= 2;
		return i;
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Index getLog2(Index m)
	{
		Index log2m = 0;
		while (m >>= 1)
			log2m++;
		return log2m;
	}

	// Call Cooley Tukey algorithm directly, data length must be power of 2
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void processDataLineCooleyTukey(ComplexScalar* line_buf,
																		  Index line_len,
																		  Index log_len)
	{
		eigen_assert(isPowerOfTwo(line_len));
		scramble_FFT(line_buf, line_len);
		compute_1D_Butterfly<FFTDir>(line_buf, line_len, log_len);
	}

	// Call Bluestein's FFT algorithm, m is a good composite number greater than (2 * n - 1), used as the padding length
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void processDataLineBluestein(ComplexScalar* line_buf,
																		Index line_len,
																		Index good_composite,
																		Index log_len,
																		ComplexScalar* a,
																		ComplexScalar* b,
																		const ComplexScalar* pos_j_base_powered)
	{
		Index n = line_len;
		Index m = good_composite;
		ComplexScalar* data = line_buf;

		for (Index i = 0; i < n; ++i) {
			if (FFTDir == FFT_FORWARD) {
				a[i] = data[i] * numext::conj(pos_j_base_powered[i]);
			} else {
				a[i] = data[i] * pos_j_base_powered[i];
			}
		}
		for (Index i = n; i < m; ++i) {
			a[i] = ComplexScalar(0, 0);
		}

		for (Index i = 0; i < n; ++i) {
			if (FFTDir == FFT_FORWARD) {
				b[i] = pos_j_base_powered[i];
			} else {
				b[i] = numext::conj(pos_j_base_powered[i]);
			}
		}
		for (Index i = n; i < m - n; ++i) {
			b[i] = ComplexScalar(0, 0);
		}
		for (Index i = m - n; i < m; ++i) {
			if (FFTDir == FFT_FORWARD) {
				b[i] = pos_j_base_powered[m - i];
			} else {
				b[i] = numext::conj(pos_j_base_powered[m - i]);
			}
		}

		scramble_FFT(a, m);
		compute_1D_Butterfly<FFT_FORWARD>(a, m, log_len);

		scramble_FFT(b, m);
		compute_1D_Butterfly<FFT_FORWARD>(b, m, log_len);

		for (Index i = 0; i < m; ++i) {
			a[i] *= b[i];
		}

		scramble_FFT(a, m);
		compute_1D_Butterfly<FFT_REVERSE>(a, m, log_len);

		// Do the scaling after ifft
		for (Index i = 0; i < m; ++i) {
			a[i] /= m;
		}

		for (Index i = 0; i < n; ++i) {
			if (FFTDir == FFT_FORWARD) {
				data[i] = a[i] * numext::conj(pos_j_base_powered[i]);
			} else {
				data[i] = a[i] * pos_j_base_powered[i];
			}
		}
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static void scramble_FFT(ComplexScalar* data, Index n)
	{
		eigen_assert(isPowerOfTwo(n));
		Index j = 1;
		for (Index i = 1; i < n; ++i) {
			if (j > i) {
				std::swap(data[j - 1], data[i - 1]);
			}
			Index m = n >> 1;
			while (m >= 2 && j > m) {
				j -= m;
				m >>= 1;
			}
			j += m;
		}
	}

	template<int Dir>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_2(ComplexScalar* data)
	{
		ComplexScalar tmp = data[1];
		data[1] = data[0] - data[1];
		data[0] += tmp;
	}

	template<int Dir>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_4(ComplexScalar* data)
	{
		ComplexScalar tmp[4];
		tmp[0] = data[0] + data[1];
		tmp[1] = data[0] - data[1];
		tmp[2] = data[2] + data[3];
		if (Dir == FFT_FORWARD) {
			tmp[3] = ComplexScalar(0.0, -1.0) * (data[2] - data[3]);
		} else {
			tmp[3] = ComplexScalar(0.0, 1.0) * (data[2] - data[3]);
		}
		data[0] = tmp[0] + tmp[2];
		data[1] = tmp[1] + tmp[3];
		data[2] = tmp[0] - tmp[2];
		data[3] = tmp[1] - tmp[3];
	}

	template<int Dir>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_8(ComplexScalar* data)
	{
		ComplexScalar tmp_1[8];
		ComplexScalar tmp_2[8];

		tmp_1[0] = data[0] + data[1];
		tmp_1[1] = data[0] - data[1];
		tmp_1[2] = data[2] + data[3];
		if (Dir == FFT_FORWARD) {
			tmp_1[3] = (data[2] - data[3]) * ComplexScalar(0, -1);
		} else {
			tmp_1[3] = (data[2] - data[3]) * ComplexScalar(0, 1);
		}
		tmp_1[4] = data[4] + data[5];
		tmp_1[5] = data[4] - data[5];
		tmp_1[6] = data[6] + data[7];
		if (Dir == FFT_FORWARD) {
			tmp_1[7] = (data[6] - data[7]) * ComplexScalar(0, -1);
		} else {
			tmp_1[7] = (data[6] - data[7]) * ComplexScalar(0, 1);
		}
		tmp_2[0] = tmp_1[0] + tmp_1[2];
		tmp_2[1] = tmp_1[1] + tmp_1[3];
		tmp_2[2] = tmp_1[0] - tmp_1[2];
		tmp_2[3] = tmp_1[1] - tmp_1[3];
		tmp_2[4] = tmp_1[4] + tmp_1[6];
// SQRT2DIV2 = sqrt(2)/2
#define SQRT2DIV2 0.7071067811865476
		if (Dir == FFT_FORWARD) {
			tmp_2[5] = (tmp_1[5] + tmp_1[7]) * ComplexScalar(SQRT2DIV2, -SQRT2DIV2);
			tmp_2[6] = (tmp_1[4] - tmp_1[6]) * ComplexScalar(0, -1);
			tmp_2[7] = (tmp_1[5] - tmp_1[7]) * ComplexScalar(-SQRT2DIV2, -SQRT2DIV2);
		} else {
			tmp_2[5] = (tmp_1[5] + tmp_1[7]) * ComplexScalar(SQRT2DIV2, SQRT2DIV2);
			tmp_2[6] = (tmp_1[4] - tmp_1[6]) * ComplexScalar(0, 1);
			tmp_2[7] = (tmp_1[5] - tmp_1[7]) * ComplexScalar(-SQRT2DIV2, SQRT2DIV2);
		}
		data[0] = tmp_2[0] + tmp_2[4];
		data[1] = tmp_2[1] + tmp_2[5];
		data[2] = tmp_2[2] + tmp_2[6];
		data[3] = tmp_2[3] + tmp_2[7];
		data[4] = tmp_2[0] - tmp_2[4];
		data[5] = tmp_2[1] - tmp_2[5];
		data[6] = tmp_2[2] - tmp_2[6];
		data[7] = tmp_2[3] - tmp_2[7];
	}

	template<int Dir>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_1D_merge(ComplexScalar* data, Index n, Index n_power_of_2)
	{
		// Original code:
		// RealScalar wtemp = std::sin(M_PI/n);
		// RealScalar wpi =  -std::sin(2 * M_PI/n);
		const RealScalar wtemp = m_sin_PI_div_n_LUT[n_power_of_2];
		const RealScalar wpi =
			(Dir == FFT_FORWARD) ? m_minus_sin_2_PI_div_n_LUT[n_power_of_2] : -m_minus_sin_2_PI_div_n_LUT[n_power_of_2];

		const ComplexScalar wp(wtemp, wpi);
		const ComplexScalar wp_one = wp + ComplexScalar(1, 0);
		const ComplexScalar wp_one_2 = wp_one * wp_one;
		const ComplexScalar wp_one_3 = wp_one_2 * wp_one;
		const ComplexScalar wp_one_4 = wp_one_3 * wp_one;
		const Index n2 = n / 2;
		ComplexScalar w(1.0, 0.0);
		for (Index i = 0; i < n2; i += 4) {
			ComplexScalar temp0(data[i + n2] * w);
			ComplexScalar temp1(data[i + 1 + n2] * w * wp_one);
			ComplexScalar temp2(data[i + 2 + n2] * w * wp_one_2);
			ComplexScalar temp3(data[i + 3 + n2] * w * wp_one_3);
			w = w * wp_one_4;

			data[i + n2] = data[i] - temp0;
			data[i] += temp0;

			data[i + 1 + n2] = data[i + 1] - temp1;
			data[i + 1] += temp1;

			data[i + 2 + n2] = data[i + 2] - temp2;
			data[i + 2] += temp2;

			data[i + 3 + n2] = data[i + 3] - temp3;
			data[i + 3] += temp3;
		}
	}

	template<int Dir>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void compute_1D_Butterfly(ComplexScalar* data, Index n, Index n_power_of_2)
	{
		eigen_assert(isPowerOfTwo(n));
		if (n > 8) {
			compute_1D_Butterfly<Dir>(data, n / 2, n_power_of_2 - 1);
			compute_1D_Butterfly<Dir>(data + n / 2, n / 2, n_power_of_2 - 1);
			butterfly_1D_merge<Dir>(data, n, n_power_of_2);
		} else if (n == 8) {
			butterfly_8<Dir>(data);
		} else if (n == 4) {
			butterfly_4<Dir>(data);
		} else if (n == 2) {
			butterfly_2<Dir>(data);
		}
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index getBaseOffsetFromIndex(Index index, Index omitted_dim) const
	{
		Index result = 0;

		if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
			for (int i = NumDims - 1; i > omitted_dim; --i) {
				const Index partial_m_stride = m_strides[i] / m_dimensions[omitted_dim];
				const Index idx = index / partial_m_stride;
				index -= idx * partial_m_stride;
				result += idx * m_strides[i];
			}
			result += index;
		} else {
			for (Index i = 0; i < omitted_dim; ++i) {
				const Index partial_m_stride = m_strides[i] / m_dimensions[omitted_dim];
				const Index idx = index / partial_m_stride;
				index -= idx * partial_m_stride;
				result += idx * m_strides[i];
			}
			result += index;
		}
		// Value of index_coords[omitted_dim] is not determined to this step
		return result;
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index getIndexFromOffset(Index base, Index omitted_dim, Index offset) const
	{
		Index result = base + offset * m_strides[omitted_dim];
		return result;
	}

  protected:
	Index m_size;
	const FFT EIGEN_DEVICE_REF m_fft;
	Dimensions m_dimensions;
	array<Index, NumDims> m_strides;
	TensorEvaluator<ArgType, Device> m_impl;
	EvaluatorPointerType m_data;
	const Device EIGEN_DEVICE_REF m_device;

	// This will support a maximum FFT size of 2^32 for each dimension
	// m_sin_PI_div_n_LUT[i] = (-2) * std::sin(M_PI / std::pow(2,i)) ^ 2;
	const RealScalar m_sin_PI_div_n_LUT[32] = { RealScalar(0.0),
												RealScalar(-2),
												RealScalar(-0.999999999999999),
												RealScalar(-0.292893218813453),
												RealScalar(-0.0761204674887130),
												RealScalar(-0.0192147195967696),
												RealScalar(-0.00481527332780311),
												RealScalar(-0.00120454379482761),
												RealScalar(-3.01181303795779e-04),
												RealScalar(-7.52981608554592e-05),
												RealScalar(-1.88247173988574e-05),
												RealScalar(-4.70619042382852e-06),
												RealScalar(-1.17654829809007e-06),
												RealScalar(-2.94137117780840e-07),
												RealScalar(-7.35342821488550e-08),
												RealScalar(-1.83835707061916e-08),
												RealScalar(-4.59589268710903e-09),
												RealScalar(-1.14897317243732e-09),
												RealScalar(-2.87243293150586e-10),
												RealScalar(-7.18108232902250e-11),
												RealScalar(-1.79527058227174e-11),
												RealScalar(-4.48817645568941e-12),
												RealScalar(-1.12204411392298e-12),
												RealScalar(-2.80511028480785e-13),
												RealScalar(-7.01277571201985e-14),
												RealScalar(-1.75319392800498e-14),
												RealScalar(-4.38298482001247e-15),
												RealScalar(-1.09574620500312e-15),
												RealScalar(-2.73936551250781e-16),
												RealScalar(-6.84841378126949e-17),
												RealScalar(-1.71210344531737e-17),
												RealScalar(-4.28025861329343e-18) };

	// m_minus_sin_2_PI_div_n_LUT[i] = -std::sin(2 * M_PI / std::pow(2,i));
	const RealScalar m_minus_sin_2_PI_div_n_LUT[32] = { RealScalar(0.0),
														RealScalar(0.0),
														RealScalar(-1.00000000000000e+00),
														RealScalar(-7.07106781186547e-01),
														RealScalar(-3.82683432365090e-01),
														RealScalar(-1.95090322016128e-01),
														RealScalar(-9.80171403295606e-02),
														RealScalar(-4.90676743274180e-02),
														RealScalar(-2.45412285229123e-02),
														RealScalar(-1.22715382857199e-02),
														RealScalar(-6.13588464915448e-03),
														RealScalar(-3.06795676296598e-03),
														RealScalar(-1.53398018628477e-03),
														RealScalar(-7.66990318742704e-04),
														RealScalar(-3.83495187571396e-04),
														RealScalar(-1.91747597310703e-04),
														RealScalar(-9.58737990959773e-05),
														RealScalar(-4.79368996030669e-05),
														RealScalar(-2.39684498084182e-05),
														RealScalar(-1.19842249050697e-05),
														RealScalar(-5.99211245264243e-06),
														RealScalar(-2.99605622633466e-06),
														RealScalar(-1.49802811316901e-06),
														RealScalar(-7.49014056584716e-07),
														RealScalar(-3.74507028292384e-07),
														RealScalar(-1.87253514146195e-07),
														RealScalar(-9.36267570730981e-08),
														RealScalar(-4.68133785365491e-08),
														RealScalar(-2.34066892682746e-08),
														RealScalar(-1.17033446341373e-08),
														RealScalar(-5.85167231706864e-09),
														RealScalar(-2.92583615853432e-09) };
};

} // end namespace Eigen

#endif // EIGEN_CXX11_TENSOR_TENSOR_FFT_H
